I've been wanting to do something similar! No mechanical filtration? Can you have livestock without it?
Bowls like this can't carry a heavy bioload without filtration, but well planted with regular wc they can easily support snails, shrimp and some small fish.
My largest no-tech tank is a 3g moderately planted vase that's home to a hundred or more pond and rams horn snails, 3 ghost shrimp and 4 "cobra" endlers (guppy/endler hybrid).
My smallest is a 4.5" diameter wineglass with hc, xmas moss, a couple tiny ramshorns, a med sized pond snail, and 3x cherry shrimp. (Okay, the *smallest* is actually a 1" x1" x 2.5" planted acrylic box, but I don't tend to count that as "stocked" as it only has 2 tiny ramshorn snails.)